Nonexistence of global solutions for a fractional differential problem

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• 作者：M.D. Kassim ; ^{dahan@kfupm.edu.sa} ; K.M. Furati ^{kmfurati@kfupm.edu.sa} ; N.-E. Tatar ^{tatarn@kfupm.edu.sa}
• 关键词：Nonexistence ; Global solution ; Caputo fractional derivative ; Riemann&ndash ; Liouville fractional integral ; Test function method
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：314
• 期：Complete
• 页码：61-68
• 全文大小：429 K
• 卷排序：314

文摘

In this paper, we study the non-existence of non-trivial global solutions for a fractional differential inequality containing a lower order fractional derivative and a polynomial source term on the right hand side. Non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of values of the exponent involved there (ensuring non-existence) is found to depend only on the lower order derivative. This is in agreement with the integer order case. Numerical examples are given to illustrate the results.